Determination of the Number-Average Molecular Weight of Polyelectrolytes*

We developed four methods using the chain dynamics in the semidilute unentangled regime to determine the number-average molecular weight (M_n) of polyelectrolytes. Our team is collaborating to measure the correlation length (ξ) using X-ray scattering, the specific viscosity (η_sp) and relaxation time (τ) using rheometry, and the diffusion coefficient (D) using NMR diffusometry. Combining the measured properties of polyelectrolyte solutions yields the number density of chains in solution which directly determines Mn. To test the four methods, we studied five cesium polystyrene sulfonate samples that have narrow molecular weight distribution. We found that all four methods work generally well for the highest molecular weight (N = 9150). However, lower molecular weight polyelectrolytes are limited to two methods because τ cannot be obtained from the shear rate dependence of viscosity. The method using η_sp systematically underestimates M_n compared with the manufacturer’s reported value, while the method using D overestimates M_n. The deviation from the expected M_n increases for shorter chains for both methods. This observation underlines the importance of the non-uniform stretching along the chain of charged polymers which disappears in the long chain limit.